This article is cited in 3 papers

A Sharp Jackson Inequality in $L_p(\mathbb R^d)$ with Dunkl Weight

D. V. Gorbachev, V. I. Ivanov

Tula State University

Abstract: A sharp Jackson inequality in the space $L_p(\mathbb R^d)$, $1\le p<2$, with Dunkl weight is proved. The best approximation is realized by entire functions of exponential spherical type. The modulus of continuity is defined by means of a generalized shift operator bounded on $L_p$, which was constructed earlier by the authors. In the case of the unit weight, this operator coincides with the mean-value operator on the sphere.

Keywords: Dunkl transform, best approximation, generalized shift operator, modulus of continuity, Jackson inequality.

UDC: 517.5

Received: 19.10.2018

DOI: 10.4213/mzm12387

 English version: Mathematical Notes, 2019, 105:5, 657–673

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